CFA Level 1 Formulas Questions and
Answers
1. Price change based on convexity: -duration(change in yield)+1/2(convexity)(change
in yield)^2
2. Effective Duration: Required if a bond has embedded options: [(v-)-(v+)]/[2V0(change in
curve)]
3. Modified Duration: [(v-)-(v+)]/[2V0(change in yield)]
4. Future Value: PV(1+(I/Y)^N)
5. PV: FV/(1+r)^n
6. PV of perpetuity: PMT / discount rate
7. Approximate percentage price change of a bond: (-)(modified duration)(ΔYTM)
8. Nominal Risk Free: Real Risk Free + expected inflation
9. Required Return: Nominal risk free + liquidity premiums + default risk premium + maturity
risk premium
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,10. EAR: [(1+periodic rate)^N ] – 1
11. EAR continuous: e^r – 1
12. Bank discount yield: (FV - Price)/(FV) * (360/T)
13. HPY: [(P1+D1)/P0] – 1
14. EAY: (1+HPY)^(365/T) – 1
15. HPY (MMY equation): MMY * (T/360)
16. MMY: HPY * (360/T)
17. Geometric return: [(1+r1)(1+r2)(1+r3)]^(1/n) – 1
18. Time weighted return: [(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) – 1
19. Harmonic Mean: [N/(sum of (1/sample means))]
20. Position of observation: (n+1)*(k/100)
21. Excess kurtosis: Sample kurtosis - 3 (3 is normal kurtosis)
22. Mean absolute deviation: sum of: (mean - sample mean)/n-1
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, 23. Variance: (x-mean)^2/N (population) and divided by (n-1) for a sample
24. Coefficient of Variation: Sample standard deviation/sample mean
25. Sharpe Ratio: Risk of portfolio - risk free / Standard deviation of portfolio
26. Joint Probability: P(AB) = P(A|B) * P(B)
27. Addition rule: P(A or B) = P(A) + P(B) - P(AB)
28. Multiplication rule: P(A and B) = P(A)*P(B)
29. Total Probability Rule: P(A) = P(A|B1)*P(B1)...+P(A|B2)*P(B2)
30. Expected Value: P(x)*(x)
31. Covariance: P[(Ra - E(Ra) * (Rb - E(Rb)] - sum for all probabilities that sum to 1 OR
[SDa*SDb*correlation)
32. Correlation: Covariance(A,B) / SDa*SDb
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Answers
1. Price change based on convexity: -duration(change in yield)+1/2(convexity)(change
in yield)^2
2. Effective Duration: Required if a bond has embedded options: [(v-)-(v+)]/[2V0(change in
curve)]
3. Modified Duration: [(v-)-(v+)]/[2V0(change in yield)]
4. Future Value: PV(1+(I/Y)^N)
5. PV: FV/(1+r)^n
6. PV of perpetuity: PMT / discount rate
7. Approximate percentage price change of a bond: (-)(modified duration)(ΔYTM)
8. Nominal Risk Free: Real Risk Free + expected inflation
9. Required Return: Nominal risk free + liquidity premiums + default risk premium + maturity
risk premium
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,10. EAR: [(1+periodic rate)^N ] – 1
11. EAR continuous: e^r – 1
12. Bank discount yield: (FV - Price)/(FV) * (360/T)
13. HPY: [(P1+D1)/P0] – 1
14. EAY: (1+HPY)^(365/T) – 1
15. HPY (MMY equation): MMY * (T/360)
16. MMY: HPY * (360/T)
17. Geometric return: [(1+r1)(1+r2)(1+r3)]^(1/n) – 1
18. Time weighted return: [(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) – 1
19. Harmonic Mean: [N/(sum of (1/sample means))]
20. Position of observation: (n+1)*(k/100)
21. Excess kurtosis: Sample kurtosis - 3 (3 is normal kurtosis)
22. Mean absolute deviation: sum of: (mean - sample mean)/n-1
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, 23. Variance: (x-mean)^2/N (population) and divided by (n-1) for a sample
24. Coefficient of Variation: Sample standard deviation/sample mean
25. Sharpe Ratio: Risk of portfolio - risk free / Standard deviation of portfolio
26. Joint Probability: P(AB) = P(A|B) * P(B)
27. Addition rule: P(A or B) = P(A) + P(B) - P(AB)
28. Multiplication rule: P(A and B) = P(A)*P(B)
29. Total Probability Rule: P(A) = P(A|B1)*P(B1)...+P(A|B2)*P(B2)
30. Expected Value: P(x)*(x)
31. Covariance: P[(Ra - E(Ra) * (Rb - E(Rb)] - sum for all probabilities that sum to 1 OR
[SDa*SDb*correlation)
32. Correlation: Covariance(A,B) / SDa*SDb
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